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Cr3bits

!cr3bits->pwt

Update the |X86ISA|::|PWT| field of a cr3bits bit structure.

Signature
(!cr3bits->pwt pwt x) → new-x
Arguments: pwt — Guard (bitp pwt).; x — Guard (cr3bits-p x).
Returns: new-x — Type (cr3bits-p new-x).

Definitions and Theorems

Function: !cr3bits->pwt$inline

(defun !cr3bits->pwt$inline (pwt x)
 (declare (xargs :guard (and (bitp pwt) (cr3bits-p x))))
 (mbe
    :logic
    (b* ((pwt (mbe :logic (bfix pwt) :exec pwt))
         (x (cr3bits-fix x)))
      (part-install pwt x :width 1 :low 3))
    :exec (the (unsigned-byte 64)
               (logior (the (unsigned-byte 64)
                            (logand (the (unsigned-byte 64) x)
                                    (the (signed-byte 5) -9)))
                       (the (unsigned-byte 4)
                            (ash (the (unsigned-byte 1) pwt) 3))))))

Theorem: cr3bits-p-of-!cr3bits->pwt

(defthm cr3bits-p-of-!cr3bits->pwt
  (b* ((new-x (!cr3bits->pwt$inline pwt x)))
    (cr3bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr3bits->pwt$inline-of-bfix-pwt

(defthm !cr3bits->pwt$inline-of-bfix-pwt
  (equal (!cr3bits->pwt$inline (bfix pwt) x)
         (!cr3bits->pwt$inline pwt x)))

Theorem: !cr3bits->pwt$inline-bit-equiv-congruence-on-pwt

(defthm !cr3bits->pwt$inline-bit-equiv-congruence-on-pwt
  (implies (bit-equiv pwt pwt-equiv)
           (equal (!cr3bits->pwt$inline pwt x)
                  (!cr3bits->pwt$inline pwt-equiv x)))
  :rule-classes :congruence)

Theorem: !cr3bits->pwt$inline-of-cr3bits-fix-x

(defthm !cr3bits->pwt$inline-of-cr3bits-fix-x
  (equal (!cr3bits->pwt$inline pwt (cr3bits-fix x))
         (!cr3bits->pwt$inline pwt x)))

Theorem: !cr3bits->pwt$inline-cr3bits-equiv-congruence-on-x

(defthm !cr3bits->pwt$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (!cr3bits->pwt$inline pwt x)
                  (!cr3bits->pwt$inline pwt x-equiv)))
  :rule-classes :congruence)

Theorem: !cr3bits->pwt-is-cr3bits

(defthm !cr3bits->pwt-is-cr3bits
  (equal (!cr3bits->pwt pwt x)
         (change-cr3bits x :pwt pwt)))

Theorem: cr3bits->pwt-of-!cr3bits->pwt

(defthm cr3bits->pwt-of-!cr3bits->pwt
  (b* ((?new-x (!cr3bits->pwt$inline pwt x)))
    (equal (cr3bits->pwt new-x)
           (bfix pwt))))

Theorem: !cr3bits->pwt-equiv-under-mask

(defthm !cr3bits->pwt-equiv-under-mask
  (b* ((?new-x (!cr3bits->pwt$inline pwt x)))
    (cr3bits-equiv-under-mask new-x x -9)))